Eyepieces

Astronomical telescopes have standard eyepiece tubes, with which
one can use eyepieces bought separately from the telescope.
Most astronomical telescopes use eyepieces with a 1 1/4" barrel
diameter, although many amateur observers with larger telescopes
designed for viewing dim galaxies at relatively low magnification
now use eyepieces with a 2" barrel diameter. Some inexpensive
telescopes sold on the mass market use interchangeable eyepieces
whose barrel diameter is approximately .965".

In metric, these sizes are:

Inches Millimetres
0.964567" 24.5
1 1/4" 31.75
2" 50.8

The standard size for microscope eyepieces is 23mm, but there are
microscopes which use eyepieces with other sizes of barrel.

The eyepiece contains both the eye lens and the field lens that
complete a telescope.

Some very old telescopes use a threaded barrel 1 1/4" in diameter
with 16 threads to the inch;
such eyepieces are referred to as RAS thread eyepieces, as
the standard which they follow was established by the Royal
Astronomical Society in Britain.

In most eyepieces, though, the field lens is placed just slightly
past where the image from the objective comes to a focus. This allows
a graticule, a flat glass disk with measuring lines placed on
it, to be used with the eyepiece if desired for some forms of
observing.

The magnification of a telescope is determined by dividing the focal
length of the telescope by the focal length of the eyepiece. Thus,
if a telescope has a focal length of 1200 mm, an eyepiece with a focal length
of 40 mm will provide a magnification of 30x; that is, things viewed with
the telescope will look 30 times larger in each direction.

Often, a telescope is described in terms of its aperture and its
focal ratio. Thus, you might see a telescope mentioned as being a 4-inch f/12
telescope. A 4-inch telescope is (often) one with a 100mm aperture: as with
the lengths of slide rules, an "inch" is often only 25mm instead of 25.4mm.
With telescopes, as with cameras, "f/12" means that the aperture is 1/12 of
the focal length. Thus, the focal length of such a telescope would be equal
to 100mm times 12, or 1200 mm.

When you look at a printed page with a magnifying glass, it will normally
look just as bright as it did before; perhaps a little dimmer because of the
loss of light in the glass, but that is not usually noticeable (or brighter if
the light illuminating the page happens to also be concentrated by the lens,
but this isn't applicable to astronomy, since you don't see even the Moon
by the light of a lamp situated behind your telescope).

Stars, however, do look brighter through a telescope. This is because they
are so tiny, that they appear as just points of light whatever magnification
you use. When a star is made brighter, in effect it is really being enlarged
but it retains the same brightness over the now larger surface area, making
for a larger total amount of light. But since the "larger area" is still just
a point, that point is brighter.

There is, however, an upper limit to this process.

By day, a typical value for the size of the pupil of the human eye is 3mm.
At night, a fully dark-adapted eye can have the pupil dilated to about 7mm.

A pair of 7x50 binoculars (50mm aperture, 7x magnification) is an example
of the class of binocular known as a "night glass". When you divide the aperture
by the magnification, you get 7 1/7 mm. We can round this off to 7mm. The aperture
divided by the magnification yields the size of the exit pupil of
the telescope. When the size of the exit pupil matches that of the dark-adapted
eye, lowering the magnification of the telescope further won't yield brighter
stars, because not all the light from the telescope for each star can enter the
eye.

This principle is illustrated below:

In the first part of the diagram, the focal length of the objective lens of the
telescope, and the effective focal length of the eyepiece, which is the
same as the focal length of the eye lens for the design shown here where
the field lens coincides with the image plane, are shown.

From the second part of the diagram, you can see why the magnification
is proportional to the ratio of the two focal lengths. The red ray
passing through the center of the objective lens goes at such an angle
as to reach a height h from the optical axis after travelling through
a distance equal to the focal length of the objective lens.

Many rays of light go through the objective lens to be focused to form the
point defining the height of the image; the other rays are shown in green. Which
one is the one bent to be the dark green ray going through the center
of the eye lens is not important. But that lens travels at a steeper
angle; from the point on the optical axis at the center of the eye
lens, it reaches the height h after travelling through a distance equal
to the focal length of the eye lens.

Thus, if we compared the height both rays would reach after travelling
the same distance, this ray would reach a height larger than the height
the other ray would reach, and the ratio of the two heights would be the
same as the ratio of the two focal lengths.

The third part of the diagram shows why the ratio of the exit pupil
to the aperture is also given by the ratio of the two focal lengths; the rays
passing through the center of the field lens enter and leave it at the same
angles, so the distance between them at either other lens is proportional to
the distance of those lenses from it.

The fourth part of the diagram illustrates another important eyepiece
characteristic, eye relief. The exit pupil indicates the size of the
circular area that can recieve all the light collected by the telescope;
but that circular area must be situated a particular distance from the
telescope to receive that light, and that distance is known as the
eye relief of the eyepiece.

The diagram below illustrates several popular types of eyepiece:

The eyepieces are all shown oriented so that the observer's eye
is looking into them from the left side of the page.

The eyepieces are grouped by category in the diagram.
It begins with designs where the distinction
between the eye lens and the field lens is marked, row, beginning with the Huyghenian.
Beginning with the Ramsden, it continues by showing designs which are nearly symmetrical.
The last two designs consisting of a pair of achromats facing each other,
the Brandon and the Kalliscopic, are designs
especially aimed at reducing distortion.

The diagram then continues with designs from the Tolles to the König aimed at
low distortion, including particularly the Orthoscopic.

It then concludes with ambitious designs aimed at providing a wide
field of view, including the original version of the famed Nagler eyepiece.

The original version of this chart showed crown elements in a light blue color,
and flint elements in a light green; as I have more detailed information on many
of these eyepieces available, I have attempted to make the color coding somewhat
more detailed. However, there may be inaccuracies, particularly
as some of the colorings are purely conjectural, such as those of
the Brandon, the Galoc, and the wide-angle Bertele.
As well, Plössl, Orthoscopic, and Kellner eyepieces,
for example, can be made with many different types of glass.
Thus, while the original
Kellner eyepiece was designed when there were not many types of
glasses available, current Kellner eyepieces are likely to offer
improved performance with more modern glasses.

The individual eyepiece types shown, in detail, are:

The Huyghenian uses a large field lens, and a
small eye lens. In this design, the field lens, instead of lying just
past the focus of the telescope, is
placed before it, preventing a graticule from being used.

The Mittenzwey eyepiece is a small improvement
on the Huyghenian, replacing the planoconvex field lens by a meniscus lens.

The Kellner eyepiece is an inexpensive design which
follows more obvious design principles. It has a large, plain, field
lens, and an achromatic eye lens.

The French is like a Kellner, but with a three-element eye lens;
sometimes available as military surplus.

The Ramsden uses two identical planoconvex lenses of
crown glass; this design is often used and reccommended for homemade eyepieces.

The Dialsight or Symmetrical eyepiece is a simple
eyepiece, designed especially for use in telescopes with graticules, built around
two identical achromatic lenses.

The Plössl eyepiece is one of the most popular eyepieces
today. It is often used for deep-sky observing, because it offers a
comparatively wide field of view of 50 degrees.

The Brandon eyepiece, manufactured by Vernonscope,
although superficially similar to the Plössl, is specifically designed to
have optical properties similar to those of the Orthoscopic.

The Kalliscopic eyepiece is another design whose
properties are similar to the Orthoscopic.

The Tolles eyepiece was made from a single
thick piece of glass, so thick that each surface should be considered
as a lens in itself. Thus, the strongly curved surface near the eye
is the eye lens, and the less strongly curved surface is the field
lens. A groove around the lens serves as a field stop, and thus this
lens resembles the Huyghenian in principle.

The Monocentric eyepiece, consisting of a thick cemented three-element
lens whose surfaces, as the name indicates, are all parts of spheres
with a common center, was designed by Stenheil, and was an early design aimed,
like the Orthoscopic, at providing the highest-quality images.
It had a narrow field of view and lacked eye relief, but because the images
were of excellent quality, it was popular among early astronomers who
studied the planets despite the inconvenience.

The Orthoscopic eyepiece is a design due to the
noted optician Ernst Abbé. Unlike many other eyepieces,
the elements of crown glass, shown in blue, are on the outside of the
eyepiece. Crown glass is harder than flint glass (shown in green) and
is basically the same as the ordinary glass used for most purposes, although
optical glass is made more carefully to be of a higher quality;
flint glass has a higher
index of refraction, but it also has dispersion that is not only larger
than that of crown glass, but is larger proportionately than its index
of refraction. The simplest forms of flint glass
are similar in composition
to lead crystal, (but usually have an even higher proportion of lead
oxide) the "sparkle" of which is a consequence of the additional dispersion.
Thus, flint glass elements normally are of the type opposite
to the function performed by the lens, as they serve to correct chromatic
aberration.

An unusual thing about the Orthoscopic is that the eye lens has only
one element, but the field lens has three. Since, like most eyepieces,
the field lens is actually located somewhat past (to the left of, in this
diagram) the image plane, it is still possible for corrections made in
the field lens to have an effect on the image of the eyepiece.

Orthoscopic eyepieces tend to be made in high powers, as they are
chiefly used for observing the planets at high magnification. The
special feature of this design is that it causes almost no distortion
of shapes, such as barrel or pincushion distortion.

Because the crown elements are on the outside, the Orthoscopic
eyepiece has proven to be more popular than the other designs
with this property.

The Reversed Kellner eyepiece
also illustrates the principle of placing additional elements
in the field lens instead of
the eye lens to correct aberrations. The illustration here attempts to
approximate the RKE eyepiece sold by Edmund Scientific.

The König eyepiece shown here (many other eyepiece
designs are also due to Albert König)
is based on the Orthoscopic design,
but splits up the three-element field lens with one extra air
gap, so that it consists of a single eye lens, a two-element lens
in the middle, and a single field lens. This creates an additional degree of
freedom for correcting abberrations, allowing the design to be
modified to provide a wider field.

The Wide-Angle eyepiece shown here is a design illustrated
in N. Howard's Standard Handbook of Telescope Making as a wide-angle
eyepiece that can be homemade by an amateur telescope maker.

The Erfle eyepiece offers an even wider field of
view than the Plössl (about 60 degrees), and again is popular for deep-sky observing.
This design originally had five elements, but many were later offered
with six; both designs are shown. It is somewhat
more expensive, but now there are available some considerably more
expensive and complicated eyepieces for deep-sky observers, offering fields
of view as wide as 82 degrees or more. The six-element version of this design
is a modification due to Kaspereit, an associate of Heinrich Erfle.

The Galoc eyepiece is an early wide-field eyepiece, often used
in military equipment. Many modified versions of this design have been made, using
special glasses or even an aspheric surface.

The Bertele eyepiece
is one that is designed, like the Orthoscopic eyepiece, to minimize
distortion, but it also serves as the basis for several
wide-angle eyepiece types. A version currently available has a field of view of 56
degrees. Ludwig Bertele designed several other types of eyepiece,
and it likely one of the more complex designs that is the one noted by some
sources as providing an 80 degree field of view.

The Wild eyepiece provides a 70 degree field.
This eyepiece resembles, but is not identical to, one of several
designs described in a 1951 patent by Ludwig Bertele. Note the series of
progressively bent elements; this is normally a way of minimizing
spherical abberration.

The Scidmore eyepiece, designed by Wright H. Scidmore
for the U.S. military at the Frankford Arsenal in Philadelphia,
is a design that existed in the early 1960s and offered an incredible
90 degree field of view. Like the original Nagler, it used only two
kinds of glass, however, it didn't include an integral Barlow (although the
last doublet in the lens is slightly negative in power, the telescope forms
its image before the light enters the eyepiece), and it
may not have been quite as well corrected towards the edge of the field, since
it was not until the Nagler that eyepieces with such a wide angle
of view gained acceptance.

This wide angle Bertele eyepiece described in
U.S. patent 2,549,158 from 1951, also has a 90 degree field of view, and with
only six elements. The eyepiece is designed so that the image formed
by the telescope should be formed on the flat surface of the field lens,
which does have the problem that any dust on that lens will be clearly visible
rather than out of focus when using the telescope.

The wide-angle Bertele pictured next is also
described in U.S. patent 2,549,158. The image is formed within
the thick field lens in the design (the groove around that
lens serve as a field stop); thus, it passes through a concave
surface, and is expanded. This patent was, not surprisingly,
cited as prior art in the original Nagler patent.

The Dilworth eyepiece, by Don Dilworth, an optical designer
and ATM, is a very recent design with excellent corrections. It is a bit on the
bulky side, resembling the Speers-WALER in that respect, but it is an amazing
design. The image formed within the lens seems to be very close to the
air-glass surface of the fourth element from the objective; a ray trace shows
that it is sometimes inside the glass, and sometimes outside, as becomes more
visible when the exit pupil is increased. I had thought that quite strange, but
that is something which is also true of some versions of the Kellner
eyepiece.

The Nagler eyepiece, a patented design whose name is
also a trademark, available from TeleVue, is shown here in its original form
(current Nagler eyepieces use more exotic glasses, have a more advanced
design, and are, as a result, somewhat more compact for any given
focal length): this eyepiece, with its wide (82 degree) field of view and high
optical quality, even on telescopes with fast focal ratios (partly explained
by the fact that the first two elements of the eyepiece, shown here on the
right, act like a Barlow lens) is generally felt to have sparked a revolution
in deep-sky observing.

The Koehler eyepiece shown here was designed at Zeiss in 1960, and
is an example of an eyepice with a 120 degree apparent field.

Of course, many other eyepiece designs are not included here.

Having begun by showing crown glass as blue, and flint glass
as green, I decided to go further, and use color-coding to
show more detail about the type of glass used in some eyepieces.
This site,
by Peter Smith, an amateur astronomer in Australia, shows complete
construction details for some eyepieces that he has designed,
for people with a more intense interest in the subject.

The diagram has been divided up into areas representing common
glass types. The diagram basically follows the convention used
by Schott and others; the lines between Extra Dense Flint and
Double Extra Dense Flint, Hard Crown and Soft Crown,
and Light Barium Crown and Medium Barium Crown,
as used by Chance-Pilkington, are added, and the line between
Lanthanum Crown and Dense Lanthanum Crown, as used by Ohara,
is added and therefore their line, rather than that used by Schott,
is used to separate Lanthanum Flint and Dense Lanthanum Flint.
The lines between Dense Barium Crown and Extra Dense Barium Crown,
between Phosphate Crown and Borosilicate Crown, and
between Extra Light Flint and Crown Flint,
on the other hand, are ones specific to Schott.
Also, the titanium flints, which are increasing in
importance, are addtionally subdivided by dividing lines based
on one used by Ohara for their Eco Glass product line (which is
divided into categories very different from the ones on this
chart). This is done so that the colors better indicate the function
a titanium flint element performs in a lens system. Note, though,
that glasses using titanium are not confined to this low index
region.

Except for the line separating crown glasses from flint glasses,
the lines are not part of a standard, but are illustrative,
and some glass types
with designations reflecting their chemical composition may be found
in one or more of the compartments along with the type whose name
is given to the compartment.

Note that the area from A to J includes many glass types,
including many of the earliest optical glasses available.
However, this region should not be confused with the "glass line",
an area in which most optical glasses reside with respect to
a parameter not visible on a chart of index of refraction versus
dispersion, specifically partial dispersion.

Only a very few glasses, as well as substances like the mineral
fluorite, and to a lesser extent
some non-glass transparent materials such as plastics
and water, are a significant distance from the glass line, making
them useful in designing apochromatic lenses.

Because of concerns about people throwing their Kellners, if not
their Naglers, into the trash, and also due to the problem of disposing
of waste materials produced during manufacture, the optical industry is currently in a
time of transition, where many optical glasses using lead oxide to
increase their refractive index are being replaced with glasses having
different compositions not including lead. Titanium oxide, which also
allows producing glasses with lower indices of refraction for a given
dispersion, is one material used for this purpose.

In this connection, it may also
be noted that some optical components made during the Second World War
used thorium oxide, or even uranium oxide, which are radioactive, to achieve
exceptional optical properties. Such glasses have been abandoned; such is
the current advanced state of the optical industry that there are now available
glasses having a similar range of optical properties as they had posessed.

Except for the historic EK-325, from Kodak, the example glasses
are all from Schott, whose distinctive designations for glasses are
popular.